A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct^2 (a, b > 0). What is the meaning of the constant c?

Category: QuestionsA particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct^2 (a, b > 0). What is the meaning of the constant c?
Editor">Editor Staff asked 11 months ago

A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct^2 (a, b > 0). What is the meaning of the constant c?
 
(a) Uniform acceleration
 
(b) Non – uniform acceleration
 
(c) Uniform retardation
 
(d) Non – uniform retardation
 
I got this question during an interview.
 
The question is from Calculus Application in section Application of Calculus of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct answer is (a) Uniform acceleration
 
For explanation: We have, x = a + bt + ct^2  ……….(1)
 
Let, v and f be the velocity and acceleration of a particle at time t seconds.
 
Then, v = dx/dt = d(a + bt + ct^2)/dt  = b + ct   ……….(2)
 
And f = dv/dt = d(b + ct)/dt = c   ……….(3)
 
Since f = dv/dt = c, hence, c represents the uniform acceleration of the particle.